Alternative Number System

The number system used by most of the modern world today is called the decimal system, involving ten digits ("Base 10"). Sometimes, if a writer wants to portray a society as being significantly alien to our own, they will include a mention of an alternative number system for this society, with the "base" being a number other than ten.

This may be used to indicate the collective intelligence of the society that produced it, if it is portrayed as more sophisticated or more primitive than our system. There may also be an inferred correlation between the ten digits in our number system and the ten digits on the average pair of human hands. Therefore, a race of aliens with Four-Fingered Hands may use a base eight number system. Finally, it is very common for robots or other computer-based intelligences to count in base two.

In the Star Wars Expanded Universe, the Hutts use a base 8 system due to only having four fingers on each hand. Being Hutts, they don't always tell this to their business partners, most of whom use base 10.

A subversion: When Douglas Adams revealed that the question which produced the Ultimate Answer (42) was What is six times nine?, somebody pointed out that the math actually did add up, using base 13. Adams responded, "I may be a sad individual, but I don't make jokes in base 13."

The gukuy in Eric Flint's Mother of Demons count using an eight-base system.

It's never mentioned in the books themselves, or the series, but the "Gallifreyan numerals" used on the spines and chapter headings of the Doctor Who New Series Adventures (9th and 10th Doctors) are in base 7.

Not so much more "accurate" as more useful. Bulk goods are bought and sold in dozens and grosses. 12 factors into 2, 3, 4, and 6. It is far easier to cut a cake/pie into 12 pieces than ten without involving a protractor.

In Learning the World by Ken MacLeod, the aliens are four-fingered, and count in base 8. When they learn that humans use base 10, their reaction is that having a base that isn't a power of two must be awfully inconvenient.

In A Fire Upon the Deep by Vernor Vinge, the doglike Tines have two different number systems: one where they count "by legs" (in base 4) and one where they count "by fore-claws" (in base 10). Confusion between these two systems leads to the accidental meeting of two of the major characters. Amdiranifani is housed in room 33, Jefri is supposed to be imprisoned in room 15 (33 in base 4), and the guard who's taking him there uses the wrong numbering system.

On Gor, the alien species the Kurii use base-12, presumably because they have 12 digits on their "hands."

Little Fuzzy, a series begun by H. Beam Piper, uses a modified form of base 5. 1, 2, 3, 4, one hand. At 125, they've reached a hand of hands. It then goes to many, and many many. The fuzzies soon adopt the human's base 10 system.

In The Iron Standard by Henry Kuttner, the six-fingered Venusians use base-12.

Out of the Dark gives us the Shongairi, who count in base-twelve. Possibly.

Zamonien in Walter Moers' novels uses base 8. The author even created new symbols for the numbers.

In the Fighting Fantasy book Rebel Planet, the two-fingered Arcadians count in binary. Converting binary to decimal is necessary to solve a couple of puzzles, though the reader is fortunately provided with a handy grid.

Centaurians in The Pentagon War have 4 tentacle-fingers on each of 4 hands. When a Centaurian named Torra Zorra reads that a cable's diameter is 3 x 10−5 meters, we get this parenthetical aside:

(Curse the human penchant for powers of ten! Torra always had to mentally convert their numbers to base sixteen, just to get a handle on them.)

A throwaway comment in the episode "The Fifth Race" implies that the Ancients counted in base eight.

Also invoked when they nearly set off a Tobin mine by entering in the wrong code due to Daniel failing to factor in a zero into his translation. He argues the Phoenicians they were descended from never used a number zero, but Carter points out in order to program something as complex as a mine, the Tobin's would have had to have added a zero component.

"New Math" by Tom Lehrer musically works through a math problem in the style of what was once called "The New Math" in the 1960s. When he's gotten an answer (not the answer, just an answer), he tells the audience that it's not that simple, because the problem was supposed to be solved in Base 8:

But don't panic. Base 8 is just like Base 10, really -- if you're missing two fingers!

In Traveller, the various alien species use different base mathematics. The Aslan use Base 8, the Hivers use Base 16, and the Droyne use Base 6. Most of the various Human Aliens, as well as the Vargr, use Base 10.

In the final boss fight in Portal, GLaDOS gives this line after taking a missile hit:

"Two plus two equals...ten. In base four! I'm fine!"

There is a popular theory among Half Life fans that the Combine use a base-17 system, based on how prominent 17 seems to be. If nothing, it reinforces the utterly alien nature of the Combine.

The Kilrathi from Wing Commander use Base 8 for their numbering system, given that they have a total of eight fingers. For the most part this isn't really mentioned much, but it's prominent in the dates for history of the Kilrathi war from their viewpoint as done in the manual for Armada, "Voices of War".

Halo fans speculate that the Forerunners might have counted using a Base-7 counting system.

The Schoolhouse Rock music video for "Little Twelvetoes" briefly touches on the idea of what counting with a base-twelve system would be like, and demonstrates with the titular twelve-fingered alien character.

Computers work in Base 2 because the only input signals they can distinguish between are "on" and "off". Each one is called a "bit". The de facto standard of a byte establishes it as 8 bits, prompting people familiar with computer science to use the hexadecimal system (base 16) to represent a byte of information in two digits.

Ancient Mayans used a base 20 system.

Ancient Babylonians counted in base 60. This is reflected in the modern measurement of time (hours, minutes and seconds), as well as angular measure (degrees, minutes, seconds).

Vestiges of base 12 remain in English and German.

Base 12 is a rather elegant base to use (especially for fractions), since it is the smallest number which is evenly divisible by 2, 3, 4, and 6 (base 10, by contrast, is only divisible by 2 and 5). The Babylonian base 60 system actually consists of 5 sets of 12 (allowing division by 5 in addition to the others).

Vestiges of base 20 remain in English ("four score years and ten ago") and French ("quatre-vingts",[2] also in the name of the Parisian hospital Quinze-Vingts[3] which was originally founded to house 300 patients).